Yeah, it'd be like telling marathoners they have to wear a specific model of shoe. There's so many factors that go into comfort etc.

Except that the team get sponsored by a manufacturer, and it's not picked by the riders.

To an extent, and seemingly always with frames. But pro riders often use parts that aren't "sponsership approved" - they just make them all black or similar (rather than have another manfacturer's logo on them)

And the manufacturer then works with the team/riders to make sure they get a bike that works for them.

I think they're picky about who pays them the most.

They are picky about winning. Money will make all the difference if they have no preference, but if they don't like something or are slower, there's no way someone who finishes in the top three would be willing to trade more money from one sponsor for moving down in the rankings.

They get team bikes. They aren't picky.

Long gone are the days of a pro rider turning up on a relabelled bike of their choice (their bike, their sponsors' logos).

The bikes tend to be distinct enough that they are definitely riding the frame of their team sponsor, and the wheels have become similarly distinctive too (no more Lightweights disguised as Mavic).

At the amateur level, bikes are always customized by the rider to some degree. Teams are usually sponsored by both a manufacturer and a bike shop, so riders have a good source of discounted components. It's not uncommon for them to strip the bike down to the frame and rebuild it the way they like. The manufacturers also ask for feedback on the frame designs and tweak them every year. I can't imagine things are much different at the pro level.

The biggest differentiator is height. I assume taller people have more muscle power hence should be put in different category.

Most champion cyclists aren't tall. What matters isn't power, but rather power to weight ratio.

That depends on the discipline. In general, track sprinters are heavyweights, kings of the mountains are flyweights.

Frame size is actually quite important for fitting a bike to a person. However, it's certainly something that could be varied within a model, just like a shoe has different sizes, or whatever. Multiple frame sizes are available on everything but the cheapest bikes - I had a choice of frame sizes on a standard Schwinn aluminum-framed bike 15 years ago.

Given the choice of 5 high-end bikes and the ability to select a proper size I don't really see a problem.

Taller people also have more person to carry around.

The biggest challenge is aerodynamics. If you're over 6'3" and want to be at all comfortable you're going to present a much larger frontal area than someone shorter.